I don't know how old your system is but what you describe sounds like a tired power supply. They will often fail after being turned off; they just don't start the necessary oscillations to continue.

These are not hard to replace but you will need to remove the current one to learn the ratings of the supply.
It only requires a Phillips screw driver to remove four screws holding the case in and then skin some knuckles pulling plugs.
If you are paranoid (not that there's anything wrong with that ;-) ), mark the connectors before pulling them so you have a 'guide' for plugging in the new one.

Power output will be on a label and the total wattage rating is the info you need; will read something like 350W or 450W.
The individual voltages and currents often listed are scaled up or down depending on the total power output so the total is all that is needed.

Very good supplies can be had for under $100 US and a typical commodity supply (kinda like the one that failed) can be had for as little as $10 +S&H on eBay.
Before the decay of the dollar, I bought these (350W) for $5.
They are repairable but . . .why?

These are the cheapest built part of your system and often the least reliable.
If you want one that will outlast your interest in the system, check out PC Power and Cooling.

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Open it up again. Take the video card out. Take the Ram out. Unplug the hard drive. Unplug the other drives. Unplug the network card(s). And unplug anything else that is tied to the motherboard. Now plug it all back in snugly.Finally,turn it on. It should be fixed.

A lot of those E-Machines used a small power supply (150 to 180 watts) and were known to have a failure rate. There is a way to check them by jumping across a two connector wires on the end that plugs into the Motherboard. Let me know if you want try this.

It sounds as if your power supply is having issues, I would recommend replacing it. If your good with computers, you can test the power supply:
1. Open the computer tower.
2. Find the main plug which runs from the power supply to the motherboard.
3. There should be 16 wires.
4. Find the green wire, short it to the black wire with a paper clip.
5. If the computer seems to turn on, its your motherboard having issues and you will probably need a new computer. If it does not turn on, your power supply has failed, and you need to replace it.
I hope this helps!

The green light is most likely your lan card/port. If the cord/outlet are sparking when you plug it in, I would say try plugging something else into that socket, if you get the same spark, I'd call an electrician. Also try plugging the pc into a different outlet. As far as the computer, if its not the outlet then it is the power supply, your motherboard may be fried in the process but if this isn't an issue with that outlet, then you should take it in to a shop.

you can try unplug the pc open the case and take out the power supply connection from the mother board wait a while and put it back in and try another power outlet and try it on a ups if u have one. or try unplugging all the components at the back of the pc connecting back only the mouse,keyboard and monitor and try it. then, if that does not work try removing the cpu and place it firmly back into the slot or socket also the memory. GOOD LUCK!!